If The Roots Of A Quadratic Equation Are Real And Equal Then The

If The Roots Of A Quadratic Equation Are Real And Equal Then The When a, b, and c are real numbers, a ≠ 0 and the discriminant is zero, then the roots α and β of the quadratic equation ax 2 bx c = 0 are real and equal. case iii: b 2 – 4ac < 0 when a, b, and c are real numbers, a ≠ 0 and the discriminant is negative, then the roots α and β of the quadratic equation ax 2 bx c = 0 are unequal. A polynomial equation whose degree is 2, is known as quadratic equation. a quadratic equation in its standard form is represented as: ax2 bx c = 0, where a, b and c are real numbers such that a ≠ 0 and x is a variable. the number of roots of a polynomial equation is equal to its degree. so, a quadratic equation has two roots.

Quadratic Equations Nature Of Roots Real And Equal Roots Youtube The roots of a quadratic equation are the values of the variable that satisfy the equation. they are also known as the "solutions" or "zeros" of the quadratic equation.for example, the roots of the quadratic equation x 2 7x 10 = 0 are x = 2 and x = 5 because they satisfy the equation. i.e., when each of them is substituted in the given equation we get 0. For example \(\sqrt{ 4}\) = 2i. so when the discriminant of a quadratic equation is less than 0, it has two roots which are distinct and complex numbers (non real). if discriminant is equal to zero. if d = 0, the quadratic equation has two equal real roots. in other words, when d = 0, the quadratic equation has only one real root. The discriminant is \({b^2} 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. roots can occur in a parabola in 3 different ways as shown in the. The graph shows the two x intercepts are ( 2, 0) and ( 3, 0). thus the two roots of the quadratic equation are ( 3, 2) nature of roots of the quadratic equation. the nature of the roots of the quadratic equation depends on the value of the discriminant as follows: if b 2 – 4ac > 0, the quadratic equation has 2 real solutions.

Ii When The Roots Of A Quadratic Equation Are Real And Equal Thenођ The discriminant is \({b^2} 4ac\), which comes from the quadratic formula and we can use this to find the nature of the roots. roots can occur in a parabola in 3 different ways as shown in the. The graph shows the two x intercepts are ( 2, 0) and ( 3, 0). thus the two roots of the quadratic equation are ( 3, 2) nature of roots of the quadratic equation. the nature of the roots of the quadratic equation depends on the value of the discriminant as follows: if b 2 – 4ac > 0, the quadratic equation has 2 real solutions. A highly dependable method for solving quadratic equations is the quadratic formula, based on the coefficients and the constant term in the equation. see example. the discriminant is used to indicate the nature of the roots that the quadratic equation will yield: real or complex, rational or irrational, and how many of each. see example. Example 4: the quad equation 2x 2 9x 7 = 0 has roots α, β. find the quadratic equation having the roots 1 α, and 1 β. solution: method 1: the quadratic equation having roots that are reciprocal to the roots of the equation ax 2 bx c = 0, is cx 2 bx a = 0. the given quadratic equation is 2x 2 9x 7 = 0.